{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3D3EAF26X37KVAB2RI4LB6E33Z","short_pith_number":"pith:3D3EAF26","canonical_record":{"source":{"id":"1811.10319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-26T12:25:35Z","cross_cats_sorted":[],"title_canon_sha256":"ec856e49093cd6b7731efe9bb218b213131f7792c784ccbb80b16f39370682f0","abstract_canon_sha256":"c6125f4daf23100a8d4e84434737c954512a4fd559fd3b9da53ce41a349e18c5"},"schema_version":"1.0"},"canonical_sha256":"d8f640175ebefeaa803a8a38b0f89bde4d6a9e6d7c9ee822fba43cef1e6c0e8e","source":{"kind":"arxiv","id":"1811.10319","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10319","created_at":"2026-05-17T23:59:56Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10319v1","created_at":"2026-05-17T23:59:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10319","created_at":"2026-05-17T23:59:56Z"},{"alias_kind":"pith_short_12","alias_value":"3D3EAF26X37K","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3D3EAF26X37KVAB2","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3D3EAF26","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3D3EAF26X37KVAB2RI4LB6E33Z","target":"record","payload":{"canonical_record":{"source":{"id":"1811.10319","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-26T12:25:35Z","cross_cats_sorted":[],"title_canon_sha256":"ec856e49093cd6b7731efe9bb218b213131f7792c784ccbb80b16f39370682f0","abstract_canon_sha256":"c6125f4daf23100a8d4e84434737c954512a4fd559fd3b9da53ce41a349e18c5"},"schema_version":"1.0"},"canonical_sha256":"d8f640175ebefeaa803a8a38b0f89bde4d6a9e6d7c9ee822fba43cef1e6c0e8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:56.814983Z","signature_b64":"ZIpy/OXkthfBUc4RBtu7h/IssCCiImxqOLNrvR8eYqcSd/JUP3mJZ4SAzoTycENw+YJYQY1ru9esStgqd9cwBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8f640175ebefeaa803a8a38b0f89bde4d6a9e6d7c9ee822fba43cef1e6c0e8e","last_reissued_at":"2026-05-17T23:59:56.814377Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:56.814377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.10319","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HUSyNG6lPKkYEAmFE5lLMjqkLdr0DFzsDqrqaz4myrq2soEzG2GZjEVIaYXQUD3i993+510OcAqQAU1imSU+Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T03:43:14.243223Z"},"content_sha256":"bde7588ec2068a90587a3047dc8184a616700883147c809ffa0bd2668deb3567","schema_version":"1.0","event_id":"sha256:bde7588ec2068a90587a3047dc8184a616700883147c809ffa0bd2668deb3567"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3D3EAF26X37KVAB2RI4LB6E33Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the cost of essentially fair clusterings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Aounon Kumar, Clemens R\\\"osner, Daniel R. Schmidt, Ioana O. Bercea, Martin Gro{\\ss}, Melanie Schmidt, Samir Khuller","submitted_at":"2018-11-26T12:25:35Z","abstract_excerpt":"Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters -- especially if the data is already biased.\n  At NIPS 2017, Chierichetti et al. proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10319","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:59:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dmvy9nXWqf3m01hWHprNiWQm0/GxbtTAHOPTeFyAWyuZKo7TGpJzHfNuX0Fhev8z4zKbcy7I9bauboKKFR4GAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T03:43:14.243897Z"},"content_sha256":"58e95d89bd649a336aadeec154cc0f92289e8b1b553d545a3fdd1ea8bb03e09c","schema_version":"1.0","event_id":"sha256:58e95d89bd649a336aadeec154cc0f92289e8b1b553d545a3fdd1ea8bb03e09c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3D3EAF26X37KVAB2RI4LB6E33Z/bundle.json","state_url":"https://pith.science/pith/3D3EAF26X37KVAB2RI4LB6E33Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3D3EAF26X37KVAB2RI4LB6E33Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-20T03:43:14Z","links":{"resolver":"https://pith.science/pith/3D3EAF26X37KVAB2RI4LB6E33Z","bundle":"https://pith.science/pith/3D3EAF26X37KVAB2RI4LB6E33Z/bundle.json","state":"https://pith.science/pith/3D3EAF26X37KVAB2RI4LB6E33Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3D3EAF26X37KVAB2RI4LB6E33Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3D3EAF26X37KVAB2RI4LB6E33Z","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c6125f4daf23100a8d4e84434737c954512a4fd559fd3b9da53ce41a349e18c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-26T12:25:35Z","title_canon_sha256":"ec856e49093cd6b7731efe9bb218b213131f7792c784ccbb80b16f39370682f0"},"schema_version":"1.0","source":{"id":"1811.10319","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.10319","created_at":"2026-05-17T23:59:56Z"},{"alias_kind":"arxiv_version","alias_value":"1811.10319v1","created_at":"2026-05-17T23:59:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.10319","created_at":"2026-05-17T23:59:56Z"},{"alias_kind":"pith_short_12","alias_value":"3D3EAF26X37K","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3D3EAF26X37KVAB2","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3D3EAF26","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:58e95d89bd649a336aadeec154cc0f92289e8b1b553d545a3fdd1ea8bb03e09c","target":"graph","created_at":"2026-05-17T23:59:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. However, this process may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters -- especially if the data is already biased.\n  At NIPS 2017, Chierichetti et al. proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both","authors_text":"Aounon Kumar, Clemens R\\\"osner, Daniel R. Schmidt, Ioana O. Bercea, Martin Gro{\\ss}, Melanie Schmidt, Samir Khuller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-26T12:25:35Z","title":"On the cost of essentially fair clusterings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.10319","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bde7588ec2068a90587a3047dc8184a616700883147c809ffa0bd2668deb3567","target":"record","created_at":"2026-05-17T23:59:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c6125f4daf23100a8d4e84434737c954512a4fd559fd3b9da53ce41a349e18c5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-26T12:25:35Z","title_canon_sha256":"ec856e49093cd6b7731efe9bb218b213131f7792c784ccbb80b16f39370682f0"},"schema_version":"1.0","source":{"id":"1811.10319","kind":"arxiv","version":1}},"canonical_sha256":"d8f640175ebefeaa803a8a38b0f89bde4d6a9e6d7c9ee822fba43cef1e6c0e8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8f640175ebefeaa803a8a38b0f89bde4d6a9e6d7c9ee822fba43cef1e6c0e8e","first_computed_at":"2026-05-17T23:59:56.814377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:56.814377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZIpy/OXkthfBUc4RBtu7h/IssCCiImxqOLNrvR8eYqcSd/JUP3mJZ4SAzoTycENw+YJYQY1ru9esStgqd9cwBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:56.814983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.10319","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bde7588ec2068a90587a3047dc8184a616700883147c809ffa0bd2668deb3567","sha256:58e95d89bd649a336aadeec154cc0f92289e8b1b553d545a3fdd1ea8bb03e09c"],"state_sha256":"c8f458c9043da3ac60308067c8971fcbb5bfc45cea01a5b9fe166c3bf796c14b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZRlvG/c+qSz3XDw9dqd3VsEOaEfqLmBMtKDfm+3tuSmX489xrmX3a3vMEJgVMXdJeuWN7h4L3Ug0hYH4o1A/Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T03:43:14.247788Z","bundle_sha256":"6a44fa6daf7c036f92fe74cb43942aadac4bcb0d16f128ac9089404cc4296291"}}